The strong limit of von Neumann subalgebras with conditional expectations

Tsukada, Makoto

doi:10.1090/S0002-9939-1985-0784175-2

The strong limit of von Neumann subalgebras with conditional expectations
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by Makoto Tsukada

Proc. Amer. Math. Soc. 94 (1985), 259-264

DOI: https://doi.org/10.1090/S0002-9939-1985-0784175-2

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Abstract:

The strong lower limit and the weak upper limit of a net of von Neumann subalgebras on which the conditional expectations exist with respect to a fixed faithful normal state are defined. The limits coincide if and only if the corresponding conditional expectations converge strongly.

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